Any of the girls can toss it, but only the one with the highest affection will. If that girls is unavailable, the ball comes from nowhere, ie if your swimming and Yuna throws the ball, it appears from nowhere. This also affects parts of the story as in who you tlk to in places like macalania, and, as is already mentioned, the affection can be increased by talking to that girl first (I always speak to Lu first, I think she's cool :P). It can also be increased by healing them in battles, so if Yuna's dying, get Tidus to cast cure on her, and her affection level will increase.